SOLUTION: A jet flew from New york to los angeles, a distance of 4200km. the speed for the return trip was 100km/hr faster than the outbound speed. if the total trip took 13 hours, what was

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Question 189603: A jet flew from New york to los angeles, a distance of 4200km. the speed for the return trip was 100km/hr faster than the outbound speed. if the total trip took 13 hours, what was the speed from new york to los angeles.
Answer by nerdybill(7384) (Show Source):
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A jet flew from New york to los angeles, a distance of 4200km. the speed for the return trip was 100km/hr faster than the outbound speed. if the total trip took 13 hours, what was the speed from new york to los angeles.
.
You will need to apply the distance formula:
d = rt
where
d is distance
r is rate or speed
t is time
.
In our case, you need to solve for 't':
t = d/r
.
Let x = outbound speed
then from "the return trip was 100km/hr faster than the outbound speed."
x + 100 = inbound speed
.
4200/x + 4200/(x+100) = 13
Multiplying both sides by x(x+100) to get rid of our denominators:
4200(x+100) + 4200x = 13(x)(x+100)
4200x+ 420000 + 4200x = 13(x^2+100x)
8400x+ 420000 = 13x^2+1300x
420000 = 13x^2 - 7100x
0 = 13x^2 - 7100x - 420000
Applying the quadratic equation yields two solutions:
x = {600, -53.8462}
.
You can toss out the negative solution leaving us with:
x = 600 km/hr outbound
.
Answer: 600 km/hr
.
Details of quadratic to follow:

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=72250000 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 600, -53.8461538461538. Here's your graph: